From 336ee081c613c205c147120f0979e9e6c0e34e42 Mon Sep 17 00:00:00 2001 From: Yadunand Prem Date: Mon, 18 Aug 2025 12:22:53 +0800 Subject: [PATCH] feat: w1 st2334 notes --- .gitmodules | 3 ++ cs4212/week-02-x86lite | 1 + st2334/main.pdf | Bin 0 -> 27795 bytes st2334/main.typ | 65 +++++++++++++++++++++++++++++++++++++++++ 4 files changed, 69 insertions(+) create mode 160000 cs4212/week-02-x86lite create mode 100644 st2334/main.pdf create mode 100644 st2334/main.typ diff --git a/.gitmodules b/.gitmodules index 6e4da16..b4894f1 100644 --- a/.gitmodules +++ b/.gitmodules @@ -4,3 +4,6 @@ [submodule "cs4212/hw1-hellocaml-yadunut"] path = cs4212/hw1-hellocaml-yadunut url = https://github.com/cs4212/hw1-hellocaml-yadunut +[submodule "cs4212/week-02-x86lite"] + path = cs4212/week-02-x86lite + url = https://github.com/cs4212/week-02-x86lite diff --git a/cs4212/week-02-x86lite b/cs4212/week-02-x86lite new file mode 160000 index 0000000..4d81e47 --- /dev/null +++ b/cs4212/week-02-x86lite @@ -0,0 +1 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[], +// author: "Yadunand Prem", +// table-of-contents: none, +// ) +#set text(lang: "en", font: ("SF Pro Display")) +#set heading(numbering: "1.") +#show raw: set text(font: "SF Mono") + += Reference +- Sample Space ($S$): Set of all possible outcomes of an experiment + - Can vary depending on the problem of interest +- Sample Point: Outcome of sample Space (Element) +- Event: Subset of sample space (Set) + +== Set Operations +- $A union B = {x : x in A "or" x in B}$ +- $A inter B = {x : x in A "and" x in B}$ +- $A' = {x : x in S "and" x in.not A}$ +- $limits(union.big)^n_(i=1) A_i = A_1 union A_2 union ... union A_n = {x: x in A_1 "or" " ... or" x in A_n}$ +- Mutually exclusive / disjoint - $A inter B = emptyset$ +- Contained - All in A are also elements in B, A is contained in B, $A subset B$ or $B supset A$ +- Equivalent - $A subset B$ and $B subset A$, then $A = B$ + +== Set Operations +- $A inter A' = emptyset$ +- $A inter emptyset = emptyset$ +- $A union A' = S$ +- $(A')' = A$ +- $A union (B inter C) = (A union B) inter (A union C)$ +- $A inter (B union C) = (A inter B) union (A inter C)$ +- $A union B = A union (B inter A')$ +- $A = (A inter B) union (A inter B')$ +- $(A_1 union A_2 union ... union A_n)' = A_1^' inter A_2^' inter ... inter A_n^'$ +- $(A_1 inter A_2 inter ... inter A_n)' = A_1^' union A_2^' union ... union A_n^'$ + +== Counting Methods +- Multiplication Principle - $r$ different experiments to be performed sequentially. Then there are $n_1n_2...n_r$ possible outcomes for $r$ experiments +- Addition Principle - experiment can be performed by $k$ different procedures. Suppose ways under different procedures *do not overlap*. Then total is $n_1 + ... + n_k$ +- *Permutation* is selection of $r$ objects out of $n$. Order is taken into consideration. + $ P^n_r = n! / (n-r)! = n(n-1)(n-2)...(n-(r-1)) $ (When $r = n, P^n_n = n!$) +- *Combination* is selection of $r$ objects out of $n$, without regard for order. + $ vec(n, r) = n!/(r!(n-r!)) = vec(n, n-r) $ + - Intuition: In terms of permutation, no of ways to choose and arrange $r$ objects out fo $n$ is $P_r^n$ + - This can be also done by the following: + - Select $r$ objects out of $n$ without regard to order: $vec(n, r)$ ways + - For each combination, permute its $r$ objects: $P^r_r$ ways + - For each combination, permute its $r$ objects: $P^r_r$ ways + - $vec(n, r) times P^r_r = P^n_r$ + +== Probability +- Probability is chance or how likely a certain event may occur. Let $A$ be an event in an experiment. $P(A)$ is to quantify how likely $A$ may occur. +=== Axioms +Probability, $P(dot)$ is a function on the collection of events in the sample space satisfying: +- For any event $A$, $0 lt.eq P(A) lt.eq 1$ +- For the sample space $P(S) = 1$ +- For any 2 mutually exclusive event $A$ and $B$, that is $A inter B = emptyset$, $P(A union B) = P(A) + P(B)$ +- $P(emptyset) = 0$ +- $P(A') = 1-P(A)$ +- $P(A) = P(A inter B) + P(A inter B')$ +- $P(A union B) = P(A) + P(B) - P(A inter B)$ +- $A subset B$, then $P(A) lt.eq P(B)$